Chapter 33 - The Nature and Propagation of Light - Problems - Exercises - Page 1106: 33.31

$\alpha$= arccos $(\frac{cos \theta}{\sqrt 2})$

I=$I_{max}$ $cos^{2}$ $\theta$ $\frac{I}{2}$=$I_{max}$ $cos^{2}$ $\beta$ Dividing both the equations, cos $\beta$= cos $\theta$/$\sqrt 2$ $\beta$= arccos $(\frac{cos \theta}{\sqrt 2})$